The usual way to guarantee stability of model predictive control strategies is based on a terminal cost function and terminal set. This paper analyzes the closed loop stability problem of constrained linear systems and presents an approach when the terminal constraints are removed. This stabilizing method requires a non- empty set of optimal terminal controls which ensure the decreasing of cost function and new stabilizing condition is established by weighting the terminal cost. The shortest stabilizing and feasible horizon for given system can be determined very easily in explicit way (i.e. the intersection between set of optimal terminal controls and input constraint set is non- empty). Prediction horizon is shorter then in method with terminal constraint and this approach leads to reduction of computational complexity of optimization problem. Based on these results, practical procedures to calculate mentioned set of optimal terminal controls for SISO and MIMO systems are presented. Moreover, some extensions to infinity norm are published. Finally, the performance of predictive controller is illustrated on some examples and some comparisons are made.
| author | = | {S. Giba\v{s}t\'ikov\'a}, |
| title | = | {A Redesign of Stabilizing Conditions for Model Predictive Control}, |
| school | = | {\'UIAM FCHPT STU v Bratislave}, |
| year | = | {2010}, |
| keyword | = | {Model predictive control, Stability, Feasibility, Constraints, SISO and MIMO systems, Infinity norm}, |
| address | = | {Radlinsk\'eho 9, 812 37 Bratislava}, |
| month | = | {21. 05. 2010}, |
| annote | = | {The usual way to guarantee stability of model predictive control strategies is based on a\ terminal cost function and terminal set. This paper analyzes the closed loop stability problem of constrained linear systems and presents an approach when the terminal constraints are removed. This stabilizing method requires a\ non- empty set of optimal terminal controls which ensure the decreasing of cost function and new stabilizing condition is established by weighting the terminal cost. The shortest stabilizing and feasible horizon for given system can be determined very easily in explicit way (i.e. the intersection between set of optimal terminal controls and input constraint set is non- empty). Prediction horizon is shorter then in method with terminal constraint and this approach leads to reduction of computational complexity of optimization problem. Based on these results, practical procedures to calculate mentioned set of optimal terminal controls for SISO and MIMO systems are presented. Moreover, some extensions to infinity norm are published. Finally, the performance of predictive controller is illustrated on some examples and some comparisons are made.}, |
| supervisor | = | {prof. Ing. Michal Kvasnica, PhD.}, |
| url | = | {https://www.uiam.sk/assets/publication_info.php?id_pub=946} |